Answer to Question #259344 in Statistics and Probability for kjkjkj

Question #259344

A sample of 81 observations has a mean 23 and standard deviation                                

 3.6, Test the Null Hypothesis H0 : μ = 25 against the alternative

 H1:  μ < 25, assuming α = .01


1
Expert's answer
2021-11-01T16:10:31-0400

n=81xˉ=23s=3.6H0:μ=25H1:μ<25n=81 \\ \bar{x} = 23 \\ s = 3.6 \\ H_0: \mu = 25 \\ H_1: \mu < 25

Test-statistic

t=xˉμs/nt=23253.6/81=20.4333=1.566α=0.01df=n1=811=80t= \frac{\bar{x} - \mu}{s / \sqrt{n}} \\ t = \frac{23-25}{3.6 / \sqrt{81} } \\ = \frac{-2}{0.4333} \\ = -1.566 \\ α=0.01 \\ df=n-1=81-1=80

One-tailed test

tcrit=2.373t_{crit} = 2.373

Reject the null hypothesis if ttcritt ≤ -t_{crit}

t=1.566>tcrit=2.373t= -1.566 > t_{crit} = -2.373

We accept the null hypothesis at 0.01 level of significance.


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